Publications
Journal articles, conference papers and workshop contributions, newest first.
Conference
CoRL
Z. Li, Y. Jin, X. J. Liu, P. Liu, V. Prasad, C. D’Eramo, G. Chalvatzaki
Conference on Robot Learning (CoRL)

Reinforcement learning (RL) has become a powerful paradigm for robot learning, particularly in sim-to-real settings, but its broader adoption remains limited by the engineering pipeline surrounding the algorithms. Building tasks, shaping rewards, and tuning hyperparameters require substantial expert effort, making RL workflows costly and difficult to scale. We introduce HARBOR, an agentic framework that frames robot RL automation as a harness-engineering problem: given a simulator codebase and a task specification, it automates the workflow from environment setup to policy training in simulation. HARBOR decomposes such high-level objectives into bounded stages executed by specialized agents through standardized commands, persistent artifacts, executable gates, and reusable knowledge, and scales iteration via decentralized parallel trials and experience learning across runs. We evaluate HARBOR across 6 benchmarks and 16 tasks in total, spanning manipulation, locomotion, and bimanual dexterous control. We demonstrate that HARBOR automates the simulation RL workflow end-to-end, designs rewards, tunes algorithms to match or improve over default configurations, and reduces engineering effort at practical token and wall-clock cost; the resulting policies can also be transferred to real robots.
Conference
IJCAI
R. Baybas, C. D’Eramo, P. Brune
International Joint Conference on Artificial Intelligence (IJCAI), Survey Track

Adaptive Reward Design (ARD) is becoming a fundamental component for Reinforcement Learning (RL) agents, as they are deployed in increasingly complex settings where a single static reward across all phases of learning is rarely sufficient. Yet, ARD is rarely studied as a coherent topic: Relevant ideas are dispersed across reward shaping, curriculum learning, intrinsic motivation, non-stationary objectives, and preference- or feedback-based learning, which obscures conceptual connections and complicates method selection. This survey provides a unified view of ARD in RL by introducing a taxonomy, organized by the primary driver of the reward variation. The taxonomy distinguishes external-feedback-driven reward updates from reward adaptations driven by endogenous within-run signals and those conditioned on exogenous context signals. Using explicit assignment rules, we place work published between 2010 and 2025 within this taxonomy. By synthesizing typical RL settings and domains at the driver level, we simplify the method selection in ARD. Further, we describe the evolution and current trends of ARD and conclude by outlining promising future research directions.
Conference
ICLR
T. Vincent, Y. Tripathi, T. Faust, Y. Oren, J. Peters, C. D’Eramo
International Conference on Learning Representations (ICLR)

The use of target networks in deep reinforcement learning is a widely popular solution to mitigate the brittleness of semi-gradient approaches and stabilize learning. However, target networks notoriously require additional memory and delay the propagation of Bellman updates compared to an ideal target-free approach. In this work, we step out of the binary choice between target-free and target-based algorithms. We introduce a new method that uses a copy of the last linear layer of the online network as a target network, while sharing the remaining parameters with the up-to-date online network. This simple modification enables us to keep the target-free's low-memory footprint while leveraging the target-based literature. We find that combining our approach with the concept of iterated Q-learning, which consists of learning consecutive Bellman updates in parallel, helps improve the sample-efficiency of target-free approaches. Our proposed method, iterated Shared Q-Learning (iS-QL), bridges the performance gap between target-free and target-based approaches across various problems while using a single Q-network, thus stepping towards resource-efficient reinforcement learning algorithms.
Conference
ICLR
A. Hendawy, H. Metternich, T. Vincent, M. Kallel, J. Peters, C. D’Eramo
International Conference on Learning Representations (ICLR)

The use of target networks is a popular approach for estimating value functions in deep Reinforcement Learning (RL). While effective, the target network remains a compromise solution that preserves stability at the cost of slowly moving targets, thus delaying learning. Conversely, using the online network as a bootstrapped target is intuitively appealing, albeit well-known to lead to unstable learning. In this work, we aim to obtain the best out of both worlds by introducing a novel update rule that computes the target using the MINimum estimate between the Target and Online network, giving rise to our method, MINTO. Through this simple, yet effective modification, we show that MINTO enables faster and stable value function learning, by mitigating the potential overestimation bias of using the online network for bootstrapping. Notably, MINTO can be seamlessly integrated into a wide range of value-based and actor-critic algorithms with a negligible cost. We evaluate MINTO extensively across diverse benchmarks, spanning online and offline RL, as well as discrete and continuous action spaces. Across all benchmarks, MINTO consistently improves performance, demonstrating its broad applicability and effectiveness.
Conference
ICML
T. Dam, P. Stenger, L. Schneider, J. Pajarinen, C. D’Eramo, O. Maillard
International Conference on Machine Learning (ICML)
Spotlight Poster (top 2% of submitted papers)

This paper introduces a novel backup strategy for Monte-Carlo Tree Search (MCTS) designed for highly stochastic and partially observable Markov decision processes. We adopt a probabilistic approach, modeling both value and action-value nodes as Gaussian distributions. We introduce a novel backup operator that computes value nodes as the Wasserstein barycenter of their action-value children nodes; thus, propagating the uncertainty of the estimate across the tree to the root node. We study our novel backup operator when using a novel combination of L^1-Wasserstein barycenter with α-divergence, by drawing a notable connection to the generalized mean backup operator. We complement our probabilistic backup operator with two sampling strategies, based on optimistic selection and Thompson sampling, obtaining our Wasserstein MCTS algorithm. We provide theoretical guarantees of asymptotic convergence to the optimal policy, and an empirical evaluation on several stochastic and partially observable environments, where our approach outperforms well-known related baselines.
Conference
ICLR
T. Vincent, F. Wahren, J. Peters, B. Belousov, C. D’Eramo
International Conference on Learning Representations (ICLR)

Deep Reinforcement Learning (RL) is well known for being highly sensitive to hyperparameters, requiring practitioners substantial efforts to optimize them for the problem at hand. This also limits the applicability of RL in real-world scenarios. In recent years, the field of automated Reinforcement Learning (AutoRL) has grown in popularity by trying to address this issue. However, these approaches typically hinge on additional samples to select well-performing hyperparameters, hindering sample-efficiency and practicality. Furthermore, most AutoRL methods are heavily based on already existing AutoML methods, which were originally developed neglecting the additional challenges inherent to RL due to its non-stationarities. In this work, we propose a new approach for AutoRL, called Adaptive Q-Network (AdaQN), that is tailored to RL to take into account the non-stationarity of the optimization procedure without requiring additional samples. AdaQN learns several Q-functions, each one trained with different hyperparameters, which are updated online using the Q-function with the smallest approximation error as a shared target. Our selection scheme simultaneously handles different hyperparameters while coping with the non-stationarity induced by the RL optimization procedure and being orthogonal to any critic-based RL algorithm. We demonstrate that AdaQN is theoretically sound and empirically validate it in MuJoCo control problems and Atari 2600 games, showing benefits in sample-efficiency, overall performance, robustness to stochasticity and training stability.
Conference
AAMAS
A. Riedmann, C. D’Eramo, B. Lugrin
International Conference on Autonomous Agents and Multiagent Systems (AAMAS)
Deep Reinforcement Learning (DRL) has proven its usefulness across various fields, sparking growing interest in applying it to education. However, most research on DRL in educational applications utilizes methods in simulation, with little evaluation involving real learners, resulting in limited evidence of their effectiveness in real-world contexts. Arguably, we consider real-world applications and in-situ experiments with users as essential for a thorough evaluation. We thus propose ResUli-RL, a novel DRL approach rooted in educational psychology, designed to provide adaptive feedback to young learners in the form of a pedagogical agent in a mobile educational app. To investigate its effectiveness, we conducted a five-week real-world evaluation with 56 primary school students, comparing ResUli-RL to an expert-designed baseline. Both groups significantly improved in reading competence, with no significant differences between them and a notable decrease in motivation in both conditions. In our aim to further improve the children's reading competence using DRL, our approach did, however, not yield the expected results. Our findings provide guidance for future work and highlight the need for real-world evaluations in education to assess the value of an educational DRL approach.
Conference
KI
A. Riedmann, J. Götz, C. D’Eramo, B. Lugrin
German Conference on Artificial Intelligence (KI)
Deep Reinforcement Learning (DRL) has proven its usefulness in various fields, such as robotic control systems, recommendation algorithms, and natural language dialogue interfaces. Recently, we have been witnessing a growing interest in applying DRL in education, with early results suggesting beneficial effects. However, the majority of research in educational applications apply methods in simulation without evaluation with real learners, thus providing scarce evidence of its effectiveness on real-world problems. Arguably, real-world applications are crucial to properly assess the validity of DRL methods. To this end, we present an approach for integrating DRL into an empirically validated digital reading application for second graders in the form of an adaptive pedagogical agent. We use DRL to tailor the agent’s feedback behavior to each child’s individual learning needs. We evaluate our approach with second graders, investigating their performance and overall motivation, and compare it to a control version of the app. Through this work, we contribute an innovative approach to the use of DRL within the context of primary education, showcasing promising results in a real-world evaluation.
Conference
ICRA
E. Sayar, Z. Bing, C. D’Eramo, S. O. Oguz, A. Knoll
IEEE International Conference on Robotics and Automation (ICRA)

Multi-goal robot manipulation tasks with sparse rewards are difficult for reinforcement learning (RL) algorithms due to the inefficiency in collecting successful experiences. Recent algorithms such as Hindsight Experience Replay (HER) expedite learning by taking advantage of failed trajectories and replacing the desired goal with one of the achieved states so that any failed trajectory can be utilized as a contribution to learning. However, HER uniformly chooses failed trajectories, without taking into account which ones might be the most valuable for learning. In this paper, we address this problem and propose a novel approach Contact Energy Based Prioritization~(CEBP) to select the samples from the replay buffer based on rich information due to contact, leveraging the touch sensors in the gripper of the robot and object displacement. Our prioritization scheme favors sampling of contact-rich experiences, which are arguably the ones providing the largest amount of information. We evaluate our proposed approach on various sparse reward robotic tasks and compare them with the state-of-the-art methods. We show that our method surpasses or performs on par with those methods on robot manipulation tasks. Finally, we deploy the trained policy from our method to a real Franka robot for a pick-and-place task. We observe that the robot can solve the task successfully. The videos and code are publicly available at: https://erdiphd.github.io/HER_force
Conference
ICLR
A. Reddi, M. Tölle, J. Peters, G. Chalvatzaki, C. D’Eramo
International Conference on Learning Representations (ICLR)
Spotlight Presentation (top 15% of accepted papers)

Robustness against adversarial attacks and distribution shifts is a long-standing goal of Reinforcement Learning (RL). To this end, Robust Adversarial Reinforcement Learning (RARL) trains a protagonist against destabilizing forces exercised by an adversary in a competitive zero-sum Markov game, whose optimal solution, i.e., rational strategy, corresponds to a Nash equilibrium. However, finding Nash equilibria requires facing complex saddle point optimization problems, which can be prohibitive to solve, especially for high-dimensional control. In this paper, we propose a novel approach for adversarial RL based on entropy regularization to ease the complexity of the saddle point optimization problem. We show that the solution of this entropy-regularized problem corresponds to a Quantal Response Equilibrium (QRE), a generalization of Nash equilibria that accounts for bounded rationality, i.e., agents sometimes play random actions instead of optimal ones. Crucially, the connection between the entropy-regularized objective and QRE enables free modulation of the rationality of the agents by simply tuning the temperature coefficient. We leverage this insight to propose our novel algorithm, Quantal Adversarial RL (QARL), which gradually increases the rationality of the adversary in a curriculum fashion until it is fully rational, easing the complexity of the optimization problem while retaining robustness. We provide extensive evidence of QARL outperforming RARL and recent baselines across several MuJoCo locomotion and navigation problems in overall performance and robustness.
Conference
ICLR
A. Hendawy, J. Peters, C. D’Eramo
International Conference on Learning Representations (ICLR)

Multi-Task Reinforcement Learning (MTRL) tackles the long-standing problem of endowing agents with skills that generalize across a variety of problems. To this end, sharing representations plays a fundamental role in capturing both unique and common characteristics of the tasks. Tasks may exhibit similarities in terms of skills, objects, or physical properties while leveraging their representations eases the achievement of a universal policy. Nevertheless, the pursuit of learning a shared set of diverse representations is still an open challenge. In this paper, we introduce a novel approach for representation learning in MTRL that encapsulates common structures among the tasks using orthogonal representations to promote diversity. Our method, named Mixture Of Orthogonal Experts (MOORE), leverages a Gram-Schmidt process to shape a shared subspace of representations generated by a mixture of experts. When task-specific information is provided, MOORE generates relevant representations from this shared subspace. We assess the effectiveness of our approach on two MTRL benchmarks, namely MiniGrid and MetaWorld, showing that MOORE surpasses related baselines and establishes a new state-of-the-art result on MetaWorld.
Conference
ICLR
G. Tiboni, P. Klink, T. Tommasi, J. Peters, C. D’Eramo, G. Chalvatzaki
International Conference on Learning Representations (ICLR)

Varying dynamics parameters in simulation is a popular Domain Randomization (DR) approach for overcoming the reality gap in Reinforcement Learning (RL). Nevertheless, DR heavily hinges on the choice of the sampling distribution of the dynamics parameters, since high variability is crucial to regularize the agent's behavior but notoriously leads to overly conservative policies when randomizing excessively. In this paper, we propose a novel approach to address sim-to-real transfer, which automatically shapes dynamics distributions during training in simulation without requiring real-world data. We introduce DOmain RAndomization via Entropy MaximizatiON (DORAEMON), a constrained optimization problem that directly maximizes the entropy of the training distribution while retaining generalization capabilities. In achieving this, DORAEMON gradually increases the diversity of sampled dynamics parameters as long as the probability of success of the current policy is sufficiently high. We empirically validate the consistent benefits of DORAEMON in obtaining highly adaptive and generalizable policies, i.e. solving the task at hand across the widest range of dynamics parameters, as opposed to representative baselines from the DR literature. Notably, we also demonstrate the Sim2Real applicability of DORAEMON through its successful zero-shot transfer in a robotic manipulation setup under unknown real-world parameters.
Conference
ICLR
M. Kallel, D. Basu, R. Akrour, C. D’Eramo
International Conference on Learning Representations (ICLR)

Deterministic policies are often preferred over stochastic ones when implemented on physical systems. They can prevent erratic and harmful behaviors while being easier to implement and interpret. However, in practice, exploration is largely performed by stochastic policies. First-order Bayesian Optimization (BO) methods offer a principled way of performing exploration using deterministic policies. This is done through a learned probabilistic model of the objective function and its gradient. Nonetheless, such approaches treat policy search as a black-box problem, and thus, neglect the reinforcement learning nature of the problem. In this work, we leverage the performance difference lemma to introduce a novel mean function for the probabilistic model. This results in augmenting BO methods with the action-value function. Hence, we call our method Augmented Bayesian Search~(ABS). Interestingly, this new mean function enhances the posterior gradient with the deterministic policy gradient, effectively bridging the gap between BO and policy gradient methods. The resulting algorithm combines the convenience of the direct policy search with the scalability of reinforcement learning. We validate ABS on high-dimensional locomotion problems and demonstrate competitive performance compared to existing direct policy search schemes.
Conference
AAAI
T. Vincent, A. Metelli, B. Belousov, J. Peters, M. Restelli, C. D’Eramo
AAAI Conference on Artificial Intelligence (AAAI)

Approximate value iteration (AVI) is a family of algorithms for reinforcement learning (RL) that aims to obtain an approximation of the optimal value function. Generally, AVI algorithms implement an iterated procedure where each step consists of (i) an application of the Bellman operator and (ii) a projection step into a considered function space. Notoriously, the Bellman operator leverages transition samples, which strongly determine its behavior, as uninformative samples can result in negligible updates or long detours, whose detrimental effects are further exacerbated by the computationally intensive projection step. To address these issues, we propose a novel alternative approach based on learning an approximate version of the Bellman operator rather than estimating it through samples as in AVI approaches. This way, we are able to (i) generalize across transition samples and (ii) avoid the computationally intensive projection step. For this reason, we call our novel operator projected Bellman operator (PBO). We formulate an optimization problem to learn PBO for generic sequential decision-making problems, and we theoretically analyze its properties in two representative classes of RL problems. Furthermore, we theoretically study our approach under the lens of AVI and devise algorithmic implementations to learn PBO in offline and online settings by leveraging neural network parameterizations. Finally, we empirically showcase the benefits of PBO w.r.t. the regular Bellman operator on several RL problems.
Conference
ICML
P. Klink, H. Yang, C. D’Eramo, J. Peters, J. Pajarinen
International Conference on Machine Learning (ICML)

Curriculum reinforcement learning (CRL) allows solving complex tasks by generating a tailored sequence of learning tasks, starting from easy ones and subsequently increasing their difficulty. Although the potential of curricula in RL has been clearly shown in a variety of works, it is less clear how to generate them for a given learning environment, resulting in a variety of methods aiming to automate this task. In this work, we focus on the idea of framing curricula as interpolations between task distributions, which has previously been shown to be a viable approach to CRL. Identifying key issues of existing methods, we frame the generation of a curriculum as a constrained optimal transport problem between task distributions. Benchmarks show that this way of curriculum generation can improve upon existing CRL methods, yielding high performance in a variety of tasks with different characteristics.
Conference
IJCNN
C. D’Eramo, G. Chalvatzaki
IEEE International Joint Conference on Neural Networks (IJCNN)
Deep Reinforcement Learning (RL) promises to lead the next advances towards the development of coveted future intelligent agents. However, the unprecedented representational power of deep function approximators, e.g. deep neural networks, comes at the cost of demanding a huge amount of experience, making deep RL impractical for applications requiring interactions with the real world. We study the problem of making use of samples in deep RL more efficiently, exploiting the desirable properties of knowledge generalization resulting from learning multiple tasks together. The outcome of our work is the coupling of multi-task RL algorithms with a task-sampling policy based on the well-known intrinsic motivation paradigm. In particular, we leverage on the notion of TD-error of Bellman updates, as an effective measure of learning progress, to prioritize sampling from the tasks contributing the most to the learning of the agent. This sampling strategy speeds up the learning of tasks for which the agent is showing progress, and postpones the learning of the remaining ones, resulting in an optimized collection of samples. Our method is supported by experimental evaluations on well-known RL control tasks, for which our approach shows superior sample-efficiency and performance compared to representative baselines. We eventually evaluate our approach on simulated control tasks based on Quanser robotics systems, confirming the advantages over the baselines also in more realistic applications.
Conference
ICLR
P. Klink, C. D’Eramo, J. Peters, J. Pajarinen
International Conference on Learning Representations (ICLR)
Curriculum value-based reinforcement learning (RL) solves a complex target task by reusing action-values across a tailored sequence of related tasks of increasing difficulty. However, finding an exact way of reusing action-values in this setting is still a poorly understood problem. In this paper, we introduce the concept of boosting to curriculum value-based RL, by approximating the action-value function as a sum of residuals trained on each task. This approach, which we refer to as boosted curriculum reinforcement learning (BCRL), has the benefit of naturally increasing the representativeness of the functional space by adding a new residual each time a new task is presented. This procedure allows reusing previous action-values while promoting expressiveness of the action-value function. We theoretically study BCRL as an approximate value iteration algorithm, discussing advantages over regular curriculum RL in terms of approximation accuracy and convergence to the optimal action-value function. Finally, we provide detailed empirical evidence of the benefits of BCRL in problems requiring curricula for accurate action-value estimation and targeted exploration.
Conference
ICML
T. Dam, C. D’Eramo, J. Peters, J. Pajarinen
International Conference on Machine Learning (ICML)

Monte-Carlo planning and Reinforcement Learning (RL) are essential to sequential decision making. The recent AlphaGo and AlphaZero algorithms have shown how to successfully combine these two paradigms in order to solve large scale sequential decision problems. These methodologies exploit a variant of the well-known UCT algorithm to trade off exploitation of good actions and exploration of unvisited states, but their empirical success comes at the cost of poor sample-efficiency and high computation time. In this paper, we overcome these limitations by considering convex regularization in Monte-Carlo Tree Search (MCTS), which has been successfully used in RL to efficiently drive exploration. First, we introduce a unifying theory on the use of generic convex regularizers in MCTS, deriving the regret analysis and providing guarantees of exponential convergence rate. Second, we exploit our theoretical framework to introduce novel regularized backup operators for MCTS, based on the relative entropy of the policy update, and on the Tsallis entropy of the policy. Finally, we empirically evaluate the proposed operators in AlphaGo and AlphaZero on problems of increasing dimensionality and branching factor, from a toy problem to several Atari games, showing their superiority w.r.t. representative baselines.
Conference
RSS
J. Urain, A. Li, P. Liu, C. D’Eramo, J. Peters
Robotics: Science and Systems (RSS)

Reactive motion generation problems are usually solved by computing actions as a sum of policies. However, these policies are independent of each other and thus, they can have conflicting behaviors when summing their contributions together. We introduce Composable Energy Policies (CEP), a novel framework for modular reactive motion generation. CEP computes the control action by optimization over the product of a set of stochastic policies. This product of policies will provide a high probability to those actions that satisfy all the components and low probability to the others. Optimizing over the product of the policies avoids the detrimental effect of conflicting behaviors between policies choosing an action that satisfies all the objectives. Besides, we show that CEP naturally adapts to the Reinforcement Learning problem allowing us to integrate, in a hierarchical fashion, any distribution as prior, from multimodal distributions to non-smooth distributions and learn a new policy given them.
Conference
ICRA
A. S. Morgan, D. Nandha, G. Chalvatzaki, C. D’Eramo, A. M. Dollar, J. Peters
IEEE International Conference on Robotics and Automation (ICRA)

Substantial advancements to model-based reinforcement learning algorithms have been impeded by the model-bias induced by the collected data, which generally hurts performance. Meanwhile, their inherent sample efficiency warrants utility for most robot applications, limiting potential damage to the robot and its environment during training. Inspired by information theoretic model predictive control and advances in deep reinforcement learning, we introduce Model Predictive Actor-Critic (MoPAC), a hybrid model-based/model-free method that combines model predictive rollouts with policy optimization as to mitigate model bias. MoPAC leverages optimal trajectories to guide policy learning, but explores via its model-free method, allowing the algorithm to learn more expressive dynamics models. This combination guarantees optimal skill learning up to an approximation error and reduces necessary physical interaction with the environment, making it suitable for real-robot training. We provide extensive results showcasing how our proposed method generally outperforms current state-of-the-art and conclude by evaluating MoPAC for learning on a physical robotic hand performing valve rotation and finger gaiting--a task that requires grasping, manipulation, and then regrasping of an object.
Conference
ICLR
C. D’Eramo, D. Tateo, A. Bonarini, M. Restelli, J. Peters
International Conference on Learning Representations (ICLR)

We study the benefit of sharing representations among tasks to enable the effective use of deep neural networks in Multi-Task Reinforcement Learning. We leverage the assumption that learning from different tasks, sharing common properties, is helpful to generalize the knowledge of them resulting in a more effective feature extraction compared to learning a single task. Intuitively, the resulting set of features offers performance benefits when used by Reinforcement Learning algorithms. We prove this by providing theoretical guarantees that highlight the conditions for which is convenient to share representations among tasks, extending the well-known finite-time bounds of Approximate Value-Iteration to the multi-task setting. In addition, we complement our analysis by proposing multi-task extensions of three Reinforcement Learning algorithms that we empirically evaluate on widely used Reinforcement Learning benchmarks showing significant improvements over the single-task counterparts in terms of sample efficiency and performance.
Conference
NeurIPS
P. Klink, C. D’Eramo, J. Peters, J. Pajarinen
Advances in Neural Information Processing Systems (NeurIPS)
Oral Presentation (top 2% of accepted papers)

Curriculum reinforcement learning (CRL) improves the learning speed and stability of an agent by exposing it to a tailored series of tasks throughout learning. Despite empirical successes, an open question in CRL is how to automatically generate a curriculum for a given reinforcement learning (RL) agent, avoiding manual design. In this paper, we propose an answer by interpreting the curriculum generation as an inference problem, where distributions over tasks are progressively learned to approach the target task. This approach leads to an automatic curriculum generation, whose pace is controlled by the agent, with solid theoretical motivation and easily integrated with deep RL algorithms. In the conducted experiments, the curricula generated with the proposed algorithm significantly improve learning performance across several environments and deep RL algorithms, matching or outperforming state-of-the-art existing CRL algorithms.
Conference
IJCAI
T. Dam, P. Klink, C. D’Eramo, J. Peters, J. Pajarinen
International Joint Conference on Artificial Intelligence (IJCAI)

We consider Monte-Carlo Tree Search (MCTS) applied to Markov Decision Processes (MDPs) and Partially Observable MDPs (POMDPs), and the well-known Upper Confidence bound for Trees (UCT) algorithm. In UCT, a tree with nodes (states) and edges (actions) is incrementally built by the expansion of nodes, and the values of nodes are updated through a backup strategy based on the average value of child nodes. However, it has been shown that with enough samples the maximum operator yields more accurate node value estimates than averaging. Instead of settling for one of these value estimates, we go a step further proposing a novel backup strategy which uses the power mean operator, which computes a value between the average and maximum value. We call our new approach Power-UCT, and argue how the use of the power mean operator helps to speed up the learning in MCTS. We theoretically analyze our method providing guarantees of convergence to the optimum. Finally, we empirically demonstrate the effectiveness of our method in well-known MDP and POMDP benchmarks, showing significant improvement in performance and convergence speed w.r.t. state of the art algorithms.
Conference
IJCNN
S. Tosatto, C. D’Eramo, J. Pajarinen, M. Restelli, J. Peters
IEEE International Joint Conference on Neural Networks (IJCNN)
Exploring high-dimensional state spaces and finding sparse rewards are central problems in reinforcement learning. Exploration strategies are frequently either naïve (e.g., simplistic-greedy or Boltzmann policies), intractable (i.e., full Bayesian treatment of reinforcement learning) or rely heavily on heuristics. The lack of a tractable but principled exploration approach unnecessarily complicates the application of reinforcement learning to a broader range of problems. Efficient exploration can be accomplished by relying on the uncertainty of the state-action value function. To obtain the uncertainty, we maintain an ensemble of value function estimates and present an optimistic Bellman equation (OBE) for such ensembles. This OBE is derived from a relative entropy maximization principle and yields an implicit exploration bonus resulting in improved exploration during action selection. The implied exploration bonus can be seen as a well-principled type of intrinsic motivation and exhibits favorable theoretical properties. OBE can be applied to a wide range of algorithms. We propose two algorithms as an application of the principle: Optimistic Q-learning and Optimistic DQN which outperform comparison methods on standard benchmarks.
Conference
IJCNN
C. D’Eramo, A. Cini, M. Restelli
IEEE International Joint Conference on Neural Networks (IJCNN)
Most of the research in Reinforcement Learning (RL) focuses on balancing exploration and exploitation. Indeed, the reasons for the success or failure of an RL algorithm often deal with the choice between the execution of exploratory actions and the exploitation of actions that are known to be good. In the context of Multi-Armed Bandits (MABs), many algorithms have addressed this dilemma. In particular, Thompson Sampling (TS) is a solution that, besides having good theoretical properties, usually works very well in practice. Unfortunately, the success of TS in MAB problems has not been replicated in RL, where it has shown to scale very poorly w.r.t. the dimensionality of the problem. Nevertheless, the application of TS in RL, instead of more myopic strategies such as ε-greedy, remains a promising solution. This paper addresses such issue proposing several algorithms to use TS in RL and deep RL in a feasible way. We present these algorithms explaining the intuitions and theoretical considerations behind them and discussing their advantages and drawbacks. Furthermore, we provide an empirical evaluation on an increasingly complex set of RL problems, showing the benefit of TS w.r.t. other sampling strategies available in classical and more recent RL literature.
Conference
ICML
S. Tosatto, M. Pirotta, C. D’Eramo, M. Restelli
International Conference on Machine Learning (ICML)

This paper is about the study of B-FQI, an Approximated Value Iteration (AVI) algorithm that exploits a boosting procedure to estimate the action-value function in reinforcement learning problems. ...
Conference
AAAI
C. D’Eramo, A. Nuara, M. Pirotta, M. Restelli
AAAI Conference on Artificial Intelligence (AAAI)

This paper is about the estimation of the maximum expected value of an infinite set of random variables.This estimation problem is relevant in many fields, like the Reinforcement Learning (RL) one.In RL it is well known that, in some stochastic environments, a bias in the estimation error can increase step-by-step the approximation error leading to large overestimates of the true action values. Recently, some approaches have been proposed to reduce such bias in order to get better action-value estimates, but are limited to finite problems.In this paper, we leverage on the recently proposed weighted estimator and on Gaussian process regression to derive a new method that is able to natively handle infinitely many random variables.We show how these techniques can be used to face both continuous state and continuous actions RL problems.To evaluate the effectiveness of the proposed approach we perform empirical comparisons with related approaches.
Conference
SSCI
D. Tateo, C. D’Eramo, A. Nuara, M. Restelli, A. Bonarini
IEEE Symposium Series on Computational Intelligence (SSCI)
In many real-world problems stochasticity is a critical issue for the learning process. The sources of stochasticity come from the transition model, the explorative component of the policy or, even worse, from noisy observations of the reward function. For a finite number of samples, traditional Reinforcement Learning (RL) methods provide biased estimates of the action-value function possibly leading to poor estimates, then propagated by the application of the Bellman operator. While some approaches assume that the estimation bias is the key problem in the learning process, we show that in some cases this assumption does not necessarily hold. We propose a method that exploits the structure of the Bellman update and the uncertainty of the estimation in order to better use the amount of information provided by the samples. We show theoretical considerations about this method and its relation w.r.t. Q-Learning. Moreover, we test it in environments available in literature in order to demonstrate its effectiveness against other algorithms that focus on bias and sample-efficiency.
Conference
ICML
C. D’Eramo, A. Nuara, M. Restelli
International Conference on Machine Learning (ICML)

This paper is about the estimation of the maximum expected value of a set of independent random variables. The performance of several learning algorithms (e.g., Q-learning) is affected by the accur...